地面沉降流固耦合模型的高效计算与反演方法研究

Land subsidence is mainly due to groundwater withdrawal, and it has been a common and serious geological hazard in China. Land subsidence induced by groundwater pumping is a complex process of water-soil coupling. Based on Biot's theory, the mathematical models for land subsidence considering this coupling effect can be constructed. However, its applicabilities are severely limited due to the high computational cost and the difficulty in obtaining required parameters. Therefore, this project mainly focuses on the efficient calculation and back analysis for parameters estimation of the coupled models, and the following foundational researches will be conducted: on the basis of the previous studies in calculation methods for groundwater flow and soil deformation, considering the characteristics of the land subsidence problem, an efficient method for the calculation of fully coupled models will be presented by combining numerical and analytical techniques; by means of parallel computing techniques, a parallelized computer program will be developed based on FORTRAN and MPI. Based on this, a method for simultaneous identification of rheological models and parameters in land subsidence calculations will be presented through integration of rheological theory, homotopy method and fuzzy theory, and the corresponding program will be further developed. The efficiency and validity of the developed algorithms and programs will be verified through comparison with field data, laboratory tests and common finite element softwares. Finally, a new computer software for land subsidence analysis can be built. The research results of this project can enrich and innovate the theories of numerical calculation for land subsidence, so as to provide technical reference for land subsidence prediction and control.

地面沉降是我国多发的重大环境地质灾害，主要由过量抽取地下水造成。抽水引起的地面沉降是一种复杂的水-土流固耦合过程，基于Biot理论可以建立考虑这种耦合效应的地面沉降模型。但是，计算工作量大、参数获取困难一直是难以克服的两个瓶颈问题。为此，项目主要围绕地面沉降流固耦合模型的高效计算与反演开展基础性研究工作：在地下水流、土体变形计算前期工作基础上，考虑地面沉降问题的特点，基于解析数值相结合的思想，建立完全耦合模型的高效计算方法；利用并行计算技术，采用FORTRAN语言和MPI库开发并行计算程序。在此基础上，结合流变理论、同伦方法与模糊理论，提出地面沉降流变模型与参数的同步反演方法，并编制反演程序；利用实测资料、室内试验和通用有限元软件，对研发的算法及程序进行合理性与高效性论证，最终开发出新的地面沉降分析软件。研究成果将丰富并创新地面沉降计算理论，为地面沉降灾害的科学预测与合理防治提供技术支持。

抽水引起的地面沉降是复杂的水-土流固耦合过程，基于Biot理论可以建立考虑水-土耦合效应的地面沉降模型。但是，地面沉降流固耦合模型一直存在计算工作量大难以应用的问题。为此，本项目围绕地面沉降的高效计算问题，建立了地面沉降耦合问题的半解析数值方法，同时考虑了土体的流变性，系统推导了求解格式，编写了FORTRAN计算程序。区别于传统有限元方法，该计算方法具有天然的解耦性，而且求解格式中不涉及数值积分，从而保证了模型的高效计算。针对半解析数值求解格式存在的解耦性，实现了并行化，利用MATLAB工具库编写了并行化计算程序，进一步提高了计算效率。以此为基础，结合大范围收敛的非线性同伦方法，提出地下水流参数反演、地面沉降黏弹性模型识别与参数反演分析方法，编写了相应反演程序。研究成果将丰富地面沉降的计算理论，为地面沉降灾害的科学预测与防治提供有效的技术手段。